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Nonparametric and arbitrage-free construction of call surfaces using l1-recovery

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  • Pierre M. Blacque-Florentin
  • Badr Missaoui

Abstract

This paper is devoted to the application of an $l_1$ -minimisation technique to construct an arbitrage-free call-option surface. We propose a nononparametric approach to obtaining model-free call option surfaces that are perfectly consistent with market quotes and free of static arbitrage. The approach is inspired from the compressed-sensing framework that is used in signal processing to deal with under-sampled signals. We address the problem of fitting the call-option surface to sparse option data. To illustrate the methodology, we proceed to the construction of the whole call-price surface of the S\&P500 options, taking into account the arbitrage possibilities in the time direction. The resulting object is a surface free of both butterfly and calendar-spread arbitrage that matches the original market points. We then move on to an FX application, namely the HKD/USD call-option surface.

Suggested Citation

  • Pierre M. Blacque-Florentin & Badr Missaoui, 2015. "Nonparametric and arbitrage-free construction of call surfaces using l1-recovery," Papers 1506.06997, arXiv.org, revised Aug 2016.
    • Handle: RePEc:arx:papers:1506.06997
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    References listed on IDEAS

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